Quantile Function

Negative binomial distribution quantile function.

The quantile function for a negative binomial random variable X returns for any k satisfying 0 <= k <= 1 the value x for which

holds, where F is the cumulative distribution function (CDF) of a negative binomial distribution with parameters r and p, where r is the number of successes until the experiment is stopped and p is the success probability. The random variable X denotes the number of failures until the r success is reached.

Installation

npm install @stdlib/stats-base-dists-negative-binomial-quantile

Usage

var quantile = require( '@stdlib/stats-base-dists-negative-binomial-quantile' );

quantile( k, r, p )

Evaluates the quantile function for a negative binomial distribution with number of successes until experiment is stopped r and success probability p.

var y = quantile( 0.9, 20.0, 0.2 );
// returns 106

y = quantile( 0.9, 20.0, 0.8 );
// returns 8

y = quantile( 0.5, 10.0, 0.4 );
// returns 14

y = quantile( 0.0, 10.0, 0.9 );
// returns 0

If provided an input value k outside of [0,1], the function returns NaN.

var y = quantile( 1.1, 20.0, 0.5 );
// returns NaN

y = quantile( -0.1, 20.0, 0.5 );
// returns NaN

While r can be interpreted as the number of successes until the experiment is stopped, the negative binomial distribution is also defined for non-integers r. In this case, r denotes shape parameter of the gamma mixing distribution.

var y = quantile( 0.5, 15.5, 0.5 );
// returns 15

y = quantile( 0.3, 7.4, 0.4 );
// returns 8

If provided a r which is not a positive number, the function returns NaN.

var y = quantile( 0.5, 0.0, 0.5 );
// returns NaN

y = quantile( 0.5, -2.0, 0.5 );
// returns NaN

If provided NaN as any argument, the function returns NaN.

var y = quantile( NaN, 20.0, 0.5 );
// returns NaN

y = quantile( 0.3, NaN, 0.5 );
// returns NaN

y = quantile( 0.3, 20.0, NaN );
// returns NaN

If provided a success probability p outside of [0,1], the function returns NaN.

var y = quantile( 0.3, 20.0, -1.0 );
// returns NaN

y = quantile( 0.3, 20.0, 1.5 );
// returns NaN

quantile.factory( r, p )

Returns a function for evaluating the quantile function for a negative binomial distribution with number of successes until experiment is stopped r and success probability p.

var myquantile = quantile.factory( 10.0, 0.5 );
var y = myquantile( 0.1 );
// returns 5

y = myquantile( 0.9 );
// returns 16

Examples

var randu = require( '@stdlib/random-base-randu' );
var quantile = require( '@stdlib/stats-base-dists-negative-binomial-quantile' );

var i;
var k;
var r;
var p;
var y;

for ( i = 0; i < 10; i++ ) {
    k = randu();
    r = randu() * 100;
    p = randu();
    y = quantile( k, r, p );
    console.log( 'k: %d, r: %d, p: %d, Q(k;r,p): %d', k.toFixed( 4 ), r.toFixed( 4 ), p.toFixed( 4 ), y );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.